Probabilistic DHP adaptive critic for nonlinear stochastic control systems

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Kárnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

Optimal Control of Heterogeneous Systems

Цветомир Цачев - В настоящия доклад се прави преглед на някои резултати от областта на оптималното управление на непрекъснатите хетерогенни системи, публикувани в периодичната научна литература в последните години. Една динамична система се нарича хетерогенна, ако всеки от нейните елементи има собствена динамиката. Тук разглеждаме оптимално управление на системи, чиято хетерогенност се описва с едномерен или двумерен параметър – на всяка стойност на параметъра отговаря съответен елемент на системата. Хетерогенните динамични системи се използват за моделиране на процеси в икономиката, епидемиологията, биологията, опазване на обществената сигурност (ограничаване на използването на наркотици) и др. Тук разглеждаме модел на оптимално инвестиране в образование на макроикономическо ниво [11], на ограничаване на последствията от разпространението на СПИН [9], на пазар на права за въглеродни емисии [3, 4] и на оптимален макроикономически растеж при повишаване на нивото на върховите технологии [1]. Ключови думи: оптимално управление, непрекъснати хетерогенни динамични системи, приложения в икономиката и епидемиолегията

Critério de correntropia no treinamento de redes fuzzy wavelet neural networks para identificação de sistemas dinâmicos não lineares

The great interest in nonlinear system identification is mainly due to the fact that a large amount of real systems are complex and need to have their nonlinearities considered so that their models can be successfully used in applications of control, prediction, inference, among others. This work evaluates the application of Fuzzy Wavelet Neural Networks (FWNN) to identify nonlinear dynamical systems subjected to noise and outliers. Generally, these elements cause negative effects on the identification procedure, resulting in erroneous interpretations regarding the dynamical behavior of the system. The FWNN combines in a single structure the ability to deal with uncertainties of fuzzy logic, the multiresolution characteristics of wavelet theory and learning and generalization abilities of the artificial neural networks. Usually, the learning procedure of these neural networks is realized by a gradient based method, which uses the mean squared error as its cost function. This work proposes the replacement of this traditional function by an Information Theoretic Learning similarity measure, called correntropy. With the use of this similarity measure, higher order statistics can be considered during the FWNN training process. For this reason, this measure is more suitable for non-Gaussian error distributions and makes the training less sensitive to the presence of outliers. In order to evaluate this replacement, FWNN models are obtained in two identification case studies: a real nonlinear system, consisting of a multisection tank, and a simulated system based on a model of the human knee joint. The results demonstrate that the application of correntropy as the error backpropagation algorithm cost function makes the identification procedure using FWNN models more robust to outliers. However, this is only achieved if the gaussian kernel width of correntropy is properly adjusted.

Optically injected multi-mode semiconductor lasers

As a device, the laser is an elegant conglomerate of elementary physical theories and state-of-the-art techniques ranging from quantum mechanics, thermal and statistical physics, material growth and non-linear mathematics. The laser has been a commercial success in medicine and telecommunication while driving the development of highly optimised devices specifically designed for a plethora of uses. Due to their low-cost and large-scale predictability many aspects of modern life would not function without the lasers. However, the laser is also a window into a system that is strongly emulated by non-linear mathematical systems and are an exceptional apparatus in the development of non-linear dynamics and is often used in the teaching of non-trivial mathematics. While single-mode semiconductor lasers have been well studied, a unified comparison of single and two-mode lasers is still needed to extend the knowledge of semiconductor lasers, as well as testing the limits of current model. Secondly, this work aims to utilise the optically injected semiconductor laser as a tool so study non-linear phenomena in other fields of study, namely ’Rogue waves’ that have been previously witnessed in oceanography and are suspected as having non-linear origins. The first half of this thesis includes a reliable and fast technique to categorise the dynamical state of optically injected two mode and single mode lasers. Analysis of the experimentally obtained time-traces revealed regions of various dynamics and allowed the automatic identification of their respective stability. The impact of this method is also extended to the detection regions containing bi-stabilities. The second half of the thesis presents an investigation into the origins of Rogue Waves in single mode lasers. After confirming their existence in single mode lasers, their distribution in time and sudden appearance in the time-series is studied to justify their name. An examination is also performed into the existence of paths that make Rogue Waves possible and the impact of noise on their distribution is also studied.

Quantification of the human postural control system to perturbations

Human standing posture is inherently unstable. The postural control system (PCS), which maintains standing posture, is composed of the sensory, musculoskeletal, and central nervous systems. Together these systems integrate sensory afferents and generate appropriate motor efferents to adjust posture. The PCS maintains the body center of mass (COM) with respect to the base of support while constantly resisting destabilizing forces from internal and external perturbations. To assess the human PCS, postural sway during quiet standing or in response to external perturbation have frequently been examined descriptively. Minimal work has been done to understand and quantify the robustness of the PCS to perturbations. Further, there have been some previous attempts to assess the dynamical systems aspects of the PCS or time evolutionary properties of postural sway. However those techniques can only provide summary information about the PCS characteristics; they cannot provide specific information about or recreate the actual sway behavior. This dissertation consists of two parts: part I, the development of two novel methods to assess the human PCS and, part II, the application of these methods. In study 1, a systematic method for analyzing the human PCS during perturbed stance was developed. A mild impulsive perturbation that subjects can easily experience in their daily lives was used. A measure of robustness of the PCS, 1/MaxSens that was based on the inverse of the sensitivity of the system, was introduced. 1/MaxSens successfully quantified the reduced robustness to external perturbations due to age-related degradation of the PCS. In study 2, a stochastic model was used to better understand the human PCS in terms of dynamical systems aspect. This methodology also has the advantage over previous methods in that the sway behavior is captured in a model that can be used to recreate the random oscillatory properties of the PCS. The invariant density which describes the long-term stationary behavior of the center of pressure (COP) was computed from a Markov chain model that was applied to postural sway data during quiet stance. In order to validate the Invariant Density Analysis (IDA), we applied the technique to COP data from different age groups. We found that older adults swayed farther from the centroid and in more stochastic and random manner than young adults. In part II, the tools developed in part I were applied to both occupational and clinical situations. In study 3, 1/MaxSens and IDA were applied to a population of firefighters to investigate the effects of air bottle configuration (weight and size) and vision on the postural stability of firefighters. We found that both air bottle weight and loss of vision, but not size of air bottle, significantly decreased balance performance and increased fall risk. In study 4, IDA was applied to data collected on 444 community-dwelling elderly adults from the MOBILIZE Boston Study. Four out of five IDA parameters were able to successfully differentiate recurrent fallers from non-fallers, while only five out of 30 more common descriptive and stochastic COP measures could distinguish the two groups. Fall history and the IDA parameter of entropy were found to be significant risk factors for falls. This research proposed a new measure for the PCS robustness (1/MaxSens) and a new technique for quantifying the dynamical systems aspect of the PCS (IDA). These new PCS analysis techniques provide easy and effective ways to assess the PCS in occupational and clinical environments.

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual o-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving nonclassical damping is proposed. An example of modal control sucessfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.

Sparse time-frequency data analysis : a multi-scale approach

In this work, we further extend the recently developed adaptive data analysis method, the Sparse Time-Frequency Representation (STFR) method. This method is based on the assumption that many physical signals inherently contain AM-FM representations. We propose a sparse optimization method to extract the AM-FM representations of such signals. We prove the convergence of the method for periodic signals under certain assumptions and provide practical algorithms specifically for the non-periodic STFR, which extends the method to tackle problems that former STFR methods could not handle, including stability to noise and non-periodic data analysis. This is a significant improvement since many adaptive and non-adaptive signal processing methods are not fully capable of handling non-periodic signals. Moreover, we propose a new STFR algorithm to study intrawave signals with strong frequency modulation and analyze the convergence of this new algorithm for periodic signals. Such signals have previously remained a bottleneck for all signal processing methods. Furthermore, we propose a modified version of STFR that facilitates the extraction of intrawaves that have overlaping frequency content. We show that the STFR methods can be applied to the realm of dynamical systems and cardiovascular signals. In particular, we present a simplified and modified version of the STFR algorithm that is potentially useful for the diagnosis of some cardiovascular diseases. We further explain some preliminary work on the nature of Intrinsic Mode Functions (IMFs) and how they can have different representations in different phase coordinates. This analysis shows that the uncertainty principle is fundamental to all oscillating signals.

Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Electronic tendering: an industry perspective

The construction industry is categorised as being an information-intensive industry and described as one of the most important industries in any developed country, facing a period of rapid and unparalleled change (Industry Science Resources 1999) (Love P.E.D., Tucker S.N. et al. 1996). Project communications are becoming increasingly complex, with a growing need and fundamental drive to collaborate electronically at project level and beyond (Olesen K. and Myers M.D. 1999; Thorpe T. and Mead S. 2001; CITE 2003). Yet, the industry is also identified as having a considerable lack of knowledge and awareness about innovative information and communication technology (ICT) and web-based communication processes, systems and solutions which may prove beneficial in the procurement, delivery and life cycle of projects (NSW Government 1998; Kajewski S. and Weippert A. 2000). The Internet has debatably revolutionised the way in which information is stored, exchanged and viewed, opening new avenues for business, which only a decade ago were deemed almost inconceivable (DCITA 1998; IIB 2002). In an attempt to put these ‘new avenues of business’ into perspective, this report provides an overall ‘snapshot’ of current public and private construction industry sector opportunities and practices in the implementation and application of web-based ICT tools, systems and processes (e-Uptake). Research found that even with a reserved uptake, the construction industry and its participating organisations are making concerted efforts (fortunately with positive results) in taking up innovative forms of doing business via the internet, including e-Tendering (making it possible to manage the entire tender letting process electronically and online) (Anumba C.J. and Ruikar K. 2002; ITCBP 2003). Furthermore, Government (often a key client within the construction industry),and with its increased tendency to transact its business electronically, undoubtedly has an effect on how various private industry consultants, contractors, suppliers, etc. do business (Murray M. 2003) – by offering a wide range of (current and anticipated) e-facilities / services, including e-Tendering (Ecommerce 2002). Overall, doing business electronically is found to have a profound impact on the way today’s construction businesses operate - streamlining existing processes, with the growth in innovative tools, such as e-Tender, offering the construction industry new responsibilities and opportunities for all parties involved (ITCBP 2003). It is therefore important that these opportunities should be accessible to as many construction industry businesses as possible (The Construction Confederation 2001). Historically, there is a considerable exchange of information between various parties during a tendering process, where accuracy and efficiency of documentation is critical. Traditionally this process is either paper-based (involving large volumes of supporting tender documentation), or via a number of stand-alone, non-compatible computer systems, usually costly to both the client and contractor. As such, having a standard electronic exchange format that allows all parties involved in an electronic tender process to access one system only via the Internet, saves both time and money, eliminates transcription errors and increases speed of bid analysis (The Construction Confederation 2001). Supporting this research project’s aims and objectives, researchers set to determine today’s construction industry ‘current state-of-play’ in relation to e-Tendering opportunities. The report also provides brief introductions to several Australian and International e-Tender systems identified during this investigation. e-Tendering, in its simplest form, is described as the electronic publishing, communicating, accessing, receiving and submitting of all tender related information and documentation via the internet, thereby replacing the traditional paper-based tender processes, and achieving a more efficient and effective business process for all parties involved (NT Governement 2000; NT Government 2000; NSW Department of Commerce 2003; NSW Government 2003). Although most of the e-Tender websites investigated at the time, maintain their tendering processes and capabilities are ‘electronic’, research shows these ‘eTendering’ systems vary from being reasonably advanced to more ‘basic’ electronic tender notification and archiving services for various industry sectors. Research also indicates an e-Tender system should have a number of basic features and capabilities, including: • All tender documentation to be distributed via a secure web-based tender system – thereby avoiding the need for collating paperwork and couriers. • The client/purchaser should be able to upload a notice and/or invitation to tender onto the system. • Notification is sent out electronically (usually via email) for suppliers to download the information and return their responses electronically (online). • During the tender period, updates and queries are exchanged through the same e-Tender system. • The client/purchaser should only be able to access the tenders after the deadline has passed. • All tender related information is held in a central database, which should be easily searchable and fully audited, with all activities recorded. • It is essential that tender documents are not read or submitted by unauthorised parties. • Users of the e-Tender system are to be properly identified and registered via controlled access. In simple terms, security has to be as good as if not better than a manual tender process. Data is to be encrypted and users authenticated by means such as digital signatures, electronic certificates or smartcards. • All parties must be assured that no 'undetected' alterations can be made to any tender. • The tenderer should be able to amend the bid right up to the deadline – whilst the client/purchaser cannot obtain access until the submission deadline has passed. • The e-Tender system may also include features such as a database of service providers with spreadsheet-based pricing schedules, which can make it easier for a potential tenderer to electronically prepare and analyse a tender. Research indicates the efficiency of an e-Tender process is well supported internationally, with a significant number, yet similar, e-Tender benefits identified during this investigation. Both construction industry and Government participants generally agree that the implementation of an automated e-Tendering process or system enhances the overall quality, timeliness and cost-effectiveness of a tender process, and provides a more streamlined method of receiving, managing, and submitting tender documents than the traditional paper-based process. On the other hand, whilst there are undoubtedly many more barriers challenging the successful implementation and adoption of an e-Tendering system or process, researchers have also identified a range of challenges and perceptions that seem to hinder the uptake of this innovative approach to tendering electronically. A central concern seems to be that of security - when industry organisations have to use the Internet for electronic information transfer. As a result, when it comes to e-Tendering, industry participants insist these innovative tendering systems are developed to ensure the utmost security and integrity. Finally, if Australian organisations continue to explore the competitive ‘dynamics’ of the construction industry, without realising the current and future, trends and benefits of adopting innovative processes, such as e-Tendering, it will limit their globalising opportunities to expand into overseas markets and allow the continuation of international firms successfully entering local markets. As such, researchers believe increased knowledge, awareness and successful implementation of innovative systems and processes raises great expectations regarding their contribution towards ‘stimulating’ the globalisation of electronic procurement activities, and improving overall business and project performances throughout the construction industry sectors and overall marketplace (NSW Government 2002; Harty C. 2003; Murray M. 2003; Pietroforte R. 2003). Achieving the successful integration of an innovative e-Tender solution with an existing / traditional process can be a complex, and if not done correctly, could lead to failure (Bourn J. 2002).

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

The influence of instructions and body-scaling as constraints on decision-making processes in team sports

Team games conceptualized as dynamical systems engender a view of emergent decision-making behaviour under constraints, although specific effects of instructional and body-scaling constraints have yet to be verified empirically. For this purpose, we studied the effects of task and individual constraints on decision-making processes in basketball. Eleven experienced female players performed 350 trials in 1 vs. 1 sub-phases of basketball in which an attacker tried to perturb the stable state of a dyad formed with a defender (i.e. break the symmetry). In Experiment 1, specific instructions (neutral, risk taking or conservative) were manipulated to observe effects on emergent behaviour of the dyadic system. When attacking players were given conservative instructions, time to cross court mid-line and variability of the attacker's trajectory were significantly greater. In Experiment 2, body-scaling of participants was manipulated by creating dyads with different height relations. When attackers were considerably taller than defenders, there were fewer occurrences of symmetry-breaking. When attackers were considerably shorter than defenders, time to cross court mid-line was significantly shorter than when dyads were composed of athletes of similar height or when attackers were considerably taller than defenders. The data exemplify how interacting task and individual constraints can influence emergent decision-making processes in team ball games.